HAL Id: inria-00072127
https://hal.inria.fr/inria-00072127
Submitted on 23 May 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,
Diagnosis of Asynchronous Discrete Event Systems, a Net Unfolding Approach
Albert Benveniste, Eric Fabre, Claude Jard, Stefan Haar
To cite this version:
Albert Benveniste, Eric Fabre, Claude Jard, Stefan Haar. Diagnosis of Asynchronous Discrete Event Systems, a Net Unfolding Approach. [Research Report] RR-4461, INRIA. 2002. �inria-00072127�
ISRN INRIA/RR--4461--FR+ENG
a p p o r t
d e r e c h e r c h e
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
Diagnosis of asynchronous discrete event systems, a net unfolding approach
Albert Benveniste, Eric Fabre, Claude Jard, and Stefan Haar
N˚4461
14th May 2002
THÈME 4
- .,0// 2143
5687:9<;>=@?A9CBEDF9<BGIHJ=K9FLM;JG8NPORQF7;J9FL:SA68QFTU9WVXQF;JU#LRQFBU4Y=K9CZ[QFB4\QFQF;^]
_#`ba>cdfeAgihkjlcmbnpo-qrjtsCu+dq$swvxqrjtcjpyzo{qzjlswu
| dyz}ky[qzaJcdJy$~sCcvbntd>xdJy
:zswdqry(hxjtCco< xxo{cvo
o{vbvFswzq | d0zdK~`bd>~`bduwewe<bgJe{qz`+Po^} ww< gikvo{wdKy
J>-bww u qz`bjpy(vo{vFd>(¡ d0¢£swrcmnlo{qzdowyz}ku~`brswubsCmy | jpo{wusCyzjly$¤k}cAdKo{uys{¢`bj|b| dJuPyqo-qzd
`jly[qzsCz}¥rdJ~>swuy[qzrm~¦qrjtsCuER¢£rswc§o{npo{rc!sw¤yzd>r¨-o-qzjlswuy>©ª«d+¢£sCntnls-¡o¬yzs{®~>o{nlnld | qrzmdP~swu~mbrzdJu~}
owvbvbrsCoC~`Ejlu¯¡$`bjp~`¯ubs«wnlsw¤own:yqo-qrdo{u
|
ubsWCntsC¤o{nqrjtcdjlyAo^¨-o{jlnlow¤bntdC©
uy[qzdJo
|
¡dmyzd@swubnl}
nlsx~>owny[qro-qrdJy°jtu~sCc¤bjluo-qrjtsCu¥¡$j±qr`²oPvo{zqzjpo{n sw
|
d>cs
|
dJn sw¢$qzjlcdwjlu²¡$`bjp~`¯nlsk~Jo{n d>¨Cd>u<qry°o{rd
sC
|
d>rd
|
jt¢Eqz`d>}owzd³d>jtqz`bdJ Cd>ubdJro{qzd
|
swuqz`bd0yro{cdyzjtqzdwksC rd>npo-qrd
|
¨kjpo°yzswcdf~>owmyzowntjtq}zdJnlo{qzjlswuE©
´ m¤owyzjl~#c%o{qz`bdJco{qzjp~>ownxqzskswnjlyRqz`o{qRs{¢µF¶>·¸xµK¹º-»t¼{½¾µ<¿{ÀsCzjlwjluo{qzjlub¢£zsCcÁqz`d(dqzrjbubd>q:rdJyzdJo{~`
owzdKob©R_#`bjpy(y[qzm | }¡#owy#cs{qrjt¨-o-qrd | ¤k}@qr`bd0vbrsw¤bnld>cÂs{¢d>¨wdJu<q~swrrd>npo-qzjlswujtuqrd>nldJ~sCccmbubjp~>o{qzjlswuy
udq¡ swrÃ%cowuo{Cd>cd>u<qK©
Ä Å<ÆXÇrÈÉ -ÊwË| dK~d>u<qrrowntjlÌ>d || jpo{wusCyzjlyJ-owyz}<u~`bzsCubswmy | jpo{wusCyzjlyJ | jlyr~rdqrddJ¨wdJuCqy[}xy[qzdJcyJ-dqrzj
udqryJbmbub¢£swn| jtuCyJbo{npo{rc~swrrd>npo-qzjlswu©
ÍpÎ&ÏzÐÒÑJÓ#Ï$ÔÕlÐÒÖ8×Ø
Ù³ÚFÛwÜÞÝßàrá<â^ßJãFÜÞÝ$ä0ÝzÜpå^æbÜçRèä-æãÞéêßàëKÜÞÝàì³ë{à¦ßKÝ[ÜIâ-æârí(ã¾Ûxàí>â^ßî%à¦ß#ßàrá<â^ßJãïð{ñ<ðòÜÞã£Û°ã¾Ûxàݦä^î%à(ã£ÜÞãÞé±à^ó
ôõEö^÷ùøFúXû¦üIý÷ùøFø8þKÿ^ÿ{û¦ü Iöxõ@ÿ^üÞûtþ ! Iöf÷" ^÷ùø$#ü%&(')Òöü8ö+*JûIöü
ÿ,'ü üÞøû-8ö%ÿ^üIû.)'ü)/-ü$' %xõ-&"û1023)%&"'.&456&ùû17,' 98:'üÞ÷ùø;<û¦ü>= ^÷? üÞø8÷6 @
A 5<5BCD+'0$ÿ^þ^øE%FG'þ&ù÷"þH%I1J1KL M ø+%NO/-ü' 1@EP@F@"RQ@/+@"%BO@SP@"R'üú÷IöT56 ^üI÷('%D@U@J÷ùøú÷Iö
DBV@VDXû¦üIüø8ÿ{û1 ^÷" %7'þC8ö^û¦ü&"Vü<W@FG ? K÷ùø.X÷ùüÞ÷ùøY'%@tü
Unité de recherche INRIA Rennes
% $*P // % /0 #/+.$ $$
o{uyf~d>qfow[qrjl~>ntd°ubswmy>qzm | jtsCuynldAvbzsC¤bnla>cd | m | jpo{CubsCy[qzjp~0vFswmb | dKyyz}xyqra>cdJy
oCy[}ku~`zsCubdJyJ©dfvbrsw¤bnla>cddJy[q¢£sCzc°mbn~>swccdmuvbrsw¤bnla>cd | dfzdK~sCuyqrzm~¦qzjlswu | dqzo-[ow~qzsCjtrd
|>qro-q0vow[qrjt | dJy o{npo{rcdJysC¤y[dJz¨>dKy>©(swmy:o | swvxqrswuy:mbu@vFswjluCq | d¨kmbd | j±q | d(npoz~sCu~mzrd>u~>d
¨ko{jld¦K~>d<mbjxyzjtCubj! d<mbd:uswmyubd cowubjlvbmbnlswuy[o{c%o{jpy |">qro{qrywnlsw¤owmx&Kd>q<mbd ubswmyEmxqrjtnljlyzswuymu
qrd>cvy#<mbjonlo%y[qzrm~¦qrmbrd |mbu sC | zdfvow[qrjtdJnI©$s{qrzdfswmbqzjlnEvbrjtu~>jtvo{nEdKyq(nld~sCu~dJvxq | d¼&%('F»±½*)>¿<¶
| dA+JyzdJowm | d%d>qzrjI©swmy,>qzm | jtsCuyfmbu¥~dJ[qo{jlu«ubsCc¤brd | d%¨-o{rjlowu<qzdJy | d@~>dvbzsC¤bnla>cdw©d>q[qzd
>qzm | d0dJy[q#cswqzjl¨&>dfvow$ntd~Jowy | d0npo~swr+>npo-qzjlswu |"o{npo{rcAdKy d>u+wdKyqrjtsCu | d0+JyzdJowmx&©
- É K Ç &. / jlowwubs<yqrjl~0oCy[}ku~`zsCubdwyz}xyqra>cdJy | jpyz~>zd>qryJ+JyzdJo{mb | dd>qzrjI | >vbnljpo{wdC~>swr0Jnlo{
qrjtsCu |ownlowzcdJyJ©
$
J É Ê {É
Æ
É É ÊI
É Iw É .Å , Å >
b©t#oC~Ã<CzsCmbu | us{qzjlswuy#swu+dqzrj&ubd>qry(owu | qr`bd>jl(mbub¢£swn| jtuCy ©f©0©0©f©0©f©0©f©0©0©©0©
b© jpyz~>myzyzjlub%owyz}<u~`bzsCubswmy | jpo{CubsCyzjpysCud>bo{cvbnld% ©0©©0©f©0©0©f©0©f©0©f©0©0©©0© K
b© ³y[}ku~`zsCubswmy | jpo{CubsCyzjpy ¢£swrc%o{n&vbrsw¤bnld>cÂy[d>q[qzjlubA©f©0©©0©f©0©0©f©0©f©0©f©0©0©©0© ^
!#"
Þ
É Þ
Å JC Å%$ Å J
@b Æ
É É ÊI
É I# Æ Å É'&
&ÒÉ .IÊ
F
(
.) É *£ ²
+
e©tntCswrj±qr`bc%y$owy#vo{q[qrd>ruc%o-q~`bjlubzmbnldJy ©0©f©0©0©f©0©f©0©©0©f©0©0©f©0©f©0©f©0©0©©0© ,
e© -³y[}ku~`zsCubswmy | jpo{CubsCyzjpy!©0©f©0©0©©0©f©0©f©0©0©f©0©f©0©©0©f©0©0©f©0©f©0©f©0©0©©0© w
e© u+jtcvbrs-¨wd | o{nlwsCzjtqz`c ¢£sw#qr`bd~>oCy[djtu+¡$`bjp~` ~>owmyzowntjtq}%jpy$zdKy[vFdJ~qzd | ©f©0©0©©0© C
.0/
x>Þ
Å Å
K21
Ê
Å
Þ
Å3&ÒÉ
b
Æ
É É
%ÊI
É
I
'4
5 ©t6o^}wdJry#o{u
|
npo-qzqzjp~d0ubd>qry¬©f©0©f©0©0©©0©f©0©f©0©0©f©0©f©0©©0©f©0©0©f©0©f©0©f©0©0©©0© 27
5 © jpo{wusCyzjly npo-q[qrjl~>dJy¬©0©f©0©f©0©f©0©0©©0©f©0©f©0©0©f©0©f©0©©0©f©0©0©f©0©f©0©f©0©0©©0©
"
ÞK&JÉ !8
° %:
uPqz`bjpyvo{vFd>¡dy[qzm | }+qz`bd | jpo{wusCyzjlys{¢qzrmbnl}+oCy[}ku~`zsCubswmyy[}xy[qzd>c%yJ©_}<vjl~Jo{ndbo{cvbnldJy³o{rd
udq¡ swrÃwd | yz}xyqrd>c%yJkyzm~`owy y[`bs-¡$ujtujt©FC© u@qz`jly CmbzdC<qz`bdfy[dJuyzsw#y[}xy[qzd>c jpy | jpyqrzjl¤bmxqrd |
local time
jlwmbrd2 "!#$#%'&(%*),+-&.0/21%3 54768$:9$:/:*;8<
jtqjlu<¨Cswnl¨wdKyyzd>¨Cd>o{nnlsk~Jo{n:yzd>uy[sCryJo-qzqroC~`bd | qzsPyzswcdubs | dJys{¢ qz`bd%ubd>q¡sCzÃ>=Þyz`bs-¡$u«jlu¬¤bnpow~Ã'?¦©
@ow~` yzd>uy[sC°`oCyAswubnl}¯oWvo{zqzjpo{n#¨kjtdJ¡s{¢³qz`bd+s-¨wdJrowntn y[}xy[qzdJc© _#`bd | jBAXd>rd>u<q%y[dJuyzswyvFsCyry[dKyzy
qr`bd>jl%s-¡$u²nlsx~>ownqrjtcdC¤bmbq%qz`bdJ}²o{rdus{q@y[}ku~`zsCubjtÌJd | © (npo{rcy%owzdrd>vFswzqzd | qzs qz`dCntsC¤o{n
yzmbvFd>r¨kjlyzsw=| d>vbjp~¦qrd | jluPCzdJ}C?#oCy[}ku~`zsCubswmyznl}wbo{u | qz`bjpyyzmbvFd>r¨<jpyzsw(vFd>z¢£swrc%y | jpo{wusCyzjlyJ© _#`jly
jpyqz`bd°q}kvbjl~Jo{no{~`bjtqzdK~¦qzmzdjluPqrd>nldJ~>swccmbujl~Jo-qzjlswuyubd>q¡sCzÃc%o{uowwdJcAdJu<qyz}ky[qzdJc%y(qrs | o^}wXswmb
cswqzjl¨^o{qzjlubWowvbvbnljl~Jo-qzjlswuED^©F@R¨Cd>u<qryc%o^}«¤Fd~>swrzdK~¦qznl}WsC | d>rd | ¤k} dKow~`¥jlu | jl¨kj| mo{nyzd>uy[sCJ¤bmxq
~>swccmubjl~Jo-qrjtubownlowzc d>¨Cd>u<qry:¨<jpoqz`dubd>q¡sCzÃA~>o{my[dKyRo0nlsCyrys{¢Eyz}<u~`bzsCubjlÌJo-qrjtsCuEwowu
|
zdKy[mn±qyRjlu
oµFº{µF¼C¶·®¶GA½¾µ½pÀ¦·8½)0o{u
|
vFsCyry[jl¤bnl}P¸xµº-¸xµX¼w¶¼%jlu<qzdJznldJo^¨kjlub°o{q qr`bd0y[mvdJz¨kjpy[sCJ©H(dJu~dCkqz`bd0rjtC`<q
vjl~qzmbrdwx¢£sC(¡$`o{q(qz`bd°y[mbvFd>r¨kjlyzsw(~>swnlntdK~¦qy>bjpy$ubswq³o%yzd<mbd>u~d0s{¢o{npo{rc%y>x¤mxqo-qz`d>o ' )*¦·8½*)-»¾»
º z¼w¶ z¶¼y[d>q$s{¢o{npo{rcyJ©
o{mbntq | jpo{CubsCyzjpyfjtu | jpyr~rdqzdd>¨wdJu<qy[}xy[qzd>c%y0`owyo{q[qrroC~¦qzd | oPy[jlwuj! ~Jo{u<qo-qzqzdJuCqrjtsCuEy[dJd%qz`bd
¡ swrÃfs{¢ 6o-¢£sC[qrmbubd#o{u | ~swÒowmxqz`bsCryJIwKLI,Kx¢£swo{uAs-¨wdJz¨kjld>¡¬s{¢qz`bd#nlj±qrd>o-qrmbzd#o{u | jlu<qzrs | m~¦qrjtsCuqzs
qr`bdyzmb¤xdJ~qJ© dK~d>u<qrrowntjlÌ>d || jpo{CubsCyzjpy#jly(owuo{nl}kÌ>d | jluMI,NK8jtu~>ntm | jtu%¤swqz` o{nlwsCzjtqz`bc%y$owu | qz`bdJjt
| jlowwubs<yzow¤bjtnljtq}vzsCvdJ[qrjtdKy0O-qr`bd$y[sCntmbqzjlswujpy¢£swrcmnlo{qzd | jtu°qzdJzc%ysw¢Fo³vbzdK~sCcAvmxqzd |°| dK~dJuCqrrowntjlÌ>d |
¼{½*)>¿wµFº-À¶ ¦E~sCuyzjly[qzjlub%s{¢:oy[d>q³s{¢R~>swccmbujl~Jo-qzjlub@c%oC~`bjtudJy$qr`o-q`o^¨wdfqr`bd>jlfyqo-qzdKy(npo{¤Fd>nld | ¤k}
yzdqyfs{¢ ¢Þo{mbntqryo{u | zdKow~qqrsPo{npo{rc sw¤yzd>r¨-o-qrjtsCuyfo{u | ~sCccmbubjp~>o{qzjlswuy7OEqr`bd%npo{ubCmo{Cd°sCzjld>u<qzd |
¢£o{cdJ¡sCzÃ%sw¢ª swub`o{cÂowu | (o{c%o | wdP=Þyzd>d-I7KQ?#jpy$myzd | o{u | qz`dy[}xy[qzdJcyo{~`bj±qrdJ~qzmbrdfjly#qr`o-q
sw¢~sCccmbubjp~>o{qzjlub°owmxqzsCc%o-qroC¡$jtqz`+oAy[}ku~`brswuswmy~swcc°mbubjp~>o-qrjtsCu@¤oCy[d | swuoCntsC¤o{nqzjlcdwbowy
rd>¨CdJowntd | ¤k}0qz`bd(oCyzyzmbcvxqrjtsCu jluRI,NKÒ©_#`bd#¡sCzÃPI,K`oCy¤dJd>udkqzdJu | d | ¤k}0qr`bd(yzowcd owmxqz`bsCry
jluSIlJK#qrs-¡ ow | ~sCuyzj| dJzjlub qr`bddTAXdJ~¦qs{¢(=Þ¤sCmbu | d | ?°~swcc°mbubjp~>o-qrjtsCu | d>npo^}xyjlu | dK~dJuCqrrowntjlÌ>d |
| jlowwubs<y[jpy>© jVU@~mbntqzjldJyfrdJyzmbntqzjlub¢£rswc ~swcc°mbubjp~>o-qrjtsCuy³jtu | jpo{wusCyzjlyo{rdAownlyzsjtuk¨wdKyqrjt<o-qrd | ¤k}
hxd>ubCmbvxqroAjluWIweKÒ©jluowntnl}wxqr`bdrdJ~>d>u<q$¡sCzÃ%sw¢_zjlvowÃ<jpyXI 5 K |
jlyr~myryzdJy#jpyzyzmbdJy#sw¢mu
|
dJ~>j
|
o{¤bjlntjtq}
¢£sCo¥~dJ[qo{jluq}<vFd s{¢
|
dK~dJuCqrrowntjlÌ>d
|
sC¤yzd>r¨^ow¤bjlntjtq}wqz`bjpy@jpyry[mbd `owy@owCo{jlu y[sCcAd rd>npo-qrjtsCu ¡$jtqz`
oCy[}ku~`zsCu<}C©#o{rswujdq#o{n8©YIKFvbrswvFsCyzdo | jBAXd>rd>u<q$o{vbvzs<ow~`ECcAsCzd³jtu@qz`bd³¢£swrcËs{¢o°y[jlcmbnpo-qrjtsCu
Z
BC\[M;^]:' IöRþ^ü&`_^aba5c.deeTf g^hi0g.jk^lmnTk^lja5f\jobp"e tû¦ü'#ÿ^üø $'.8÷ùû1 û:8ö%\qrstrÿKüIûû1 >'þ&0!' %;
'710T ÷" &"û10T0þ ^÷"'.8÷ùû1 Kø ¾ú&û¦üÞý>øW@
5
Cmbj
| d |
¤k} qz`bd«sw¤yzd>r¨wd
|
ownlowzc%yJ ¢£swo¯cAs
|
dJn³sw¢~swcc°mbubjp~>o-qrjtu²o{mxqrswc%o-qob©_#`bd y[sCntmxqrjtsCu
vzsCvs<y[d
|
s*AFdJry$o y[qo-q[qrd>cvxq(qrs%`o{u
|
ntdqz`bd0vbrsw¤ntdJcs{¢y[qro-qrd0dxvbnlsCyzjtsCu¡$`jl~` rdJyzmbntqry ¢£rswc
qr`bd0jluCqrd>rntdKo^¨kjtubAs{¢d>¨Cd>u<qry#jluk¨wswnl¨kjtu
|
jVAXd>rd>u<q~sCcAvFswud>u<qryJ©
jlowwubs<y[jpyjtu qz`bd«¢£rowcd>¡ swrà sw¢dqzrjubdq cs | d>npy`owy+o{npy[s²¤dJd>u jtuk¨wdKyqrjt<o-qrd | ¤k} y[sCcd
owmxqz`swy>© Ho | jl~>sCy[qzjpyo{u | dJzC`bdJyzdPIù {K~swuy[j| d>(¢Þo{mbntqryjtu dqrzjubdqy(jlu+qz`bd¢£swrcs{¢nlsCyry[dKy$sw
| mbvbnljl~Jo-qzjlswuyfs{¢ qzswÃCd>uy7OEqr`bjpy0jly | jBAXd>rd>u<q0¢£rswcmyzjlub dqzrjubd>qryoCy0o{u¬owyz}<u~`bzsCubswmyc%ow~`jtubd
cs | dJnI^¢£sC | jpo{CubsCyzjlyJ©Rowntd>q[qzd o{u | ~s{®o{mbqz`bsCry IC K<myzd:d>qzrjCubd>qryqzs³cs | d>nCqz`bdubswrc%o{nw¤Fd>`o^¨<jlsw
sw¢by[}xy[qzd>c%yJ-o{u | ~>swuyzj| d>oCy&¢Þowmbn±qyEqr`bd:sx~J~mbrzdJu~dsw¢bd>¨Cd>u<qryEqz`o{q | s(us{qc%o{qr~`, rjtu³~sCu | jtqzjlswuy
vzsCvdJznl}w©(_#`bd°¡sCzÃ~nlsCyzdJy[q(qzsswmby$jpy(qr`o-qs{¢jlmo@owu | ~swÒowmxqz`swyXI bK5Iù w NK8Fjtq~sCuyzj| dJry(qz`bd
dKyqrjtc%o{qzjlswus{¢qz`bd0~mzrd>u<q$c%o{rÃ<jlub°¢£zsCcsC¤y[dJz¨-o{qzjlswuyJ©
@R¨Cd>u<q~>swrzdJnlo{qzjlswuAjtu%ubd>q¡sCzðc%o{uowwd>cdJuCqRjpyqr`bdyzmb¤xdK~¦q:sw¢&o~swuy[j| d>o{¤ntd#nlj±qrd>o-qzmzdCCo{u |
oukmbc¤Fd>fs{¢ ~swccd>~jpo{nvbrs | m~¦qyfo{rd°o^¨-o{jlnlow¤bnldw©fª«dArd¢£d>qr`bd°rdJo | d>³qzsfo{ | ubdJ8Il,NK¢£sCo
yzmbr¨wdJ}w©_#`bd>rd0o{rdq¡ sc%o{jlu¢£o{cdJ¡sCzÃxy:¢£sw$csCy[q$cAd>qz`bs | y | d>¨Cd>nlswvFd | jtuqz`jly(owzdKob©_#`bd yq
sCubdrd>npo-qrdJyqzszmntd>8¤oCy[d | swf~>oCy[d>8¤owyzd | rdJowyzswujtubFowu«owvbvbrsCow~` ¨Cd>r} | jBAXd>rd>u<q¢£zsCc qz`bdAswubd
¡ dyqrm | }W`d>rdw©°_#`dyzdJ~>swu | swud°myzdJy0o~>owmyro{ncs | d>n8jlu«¡$`bjp~`«qz`bdrd>npo-qzjlswu«¤d>q¡dJd>u«¢Þo{mbntq}
y[qro{qzdKy0o{u | o{npo{rcdJ¨wd>u<qyfjly0cs | dJntnld | ©_#`bdo{zqzjp~nldJyf¤k} sCmbntsCmxqroCyfdqownI©FINKLI7K5Iù 5 K:¤dJntsCub+qzs
qr`bjpy#¢Þo{cjlnt}Cbowy#¡ d>nlnEowy$$sCÌ 0o{u | sw | jld>XIwK¡$`jl~`zdJntjldJy#sCuqr`bd | jpo{CubsCyzd>$o{vvbzs<ow~`@sw¢ IwNK8©
_#`d³~>oCy[ds{¢Ed>¨Cd>u<q~>swrzdJnlo{qzjlswujtuubdq¡ swrÃc%o{uo{wdJcd>u<qo{npyzscs{qzjl¨-o-qrd | qr`bd³yzd>rjtdKyRsw¢Evo{vFd>yR¤k}
o{¤brdfdqownI©YI
5
KLItKLIù KÒbswu¡$`bjp~`qr`bd0vbrdJyzd>u<q$vo{vFd>$rd>nljtdKy>©
³yRyzowj| ¤Fd¢£sCzdCwswmvbzdKy[dJu<qowvbvbrsCoC~`°¡#owycs{qrjt¨-o{qzd | ¤k}qr`bd$vbrsw¤bnld>c s{¢F¢Þo{mbntqRc%o{uowwdJcAdJu<q
jluqzdJntdK~swcc°mbubjp~>o-qrjtsCuy#ubd>q¡sCzÃxyJkyzsj±q(jpy$¡ swzqz` | jpyz~>myzyzjlub`bs-¡ qr`bjly~swu<qrdkq(cs{qzjl¨-o-qrd | y[sCcd
sw¢swmb~`swjp~dJyJ© y³y[dJd>u+¢£rswc swmb(¤jt¤bnljlswwo{v`bjl~Jo{n | jlyr~myryzjtsCuEbq¡ s@~npowyry[dKy$s{¢RowvbvbrsCow~`dJy#¡ d>rd
o^¨-owjtnpo{¤bnldw<qrs%`o{u
|
ntdqz`d
|
jlowwubs<y[jpy s{¢owyz}<u~`bzsCubswmyyz}xyqrd>c%y>©
vFsCyry[jl¤bnldo{vvbzs<ow~`¥¡ swmbn
|
~>swuyzjpyqAjtu~swuyqrzm~qzjlub¬o
|
jpo{CubsCyzd>°jtu²qz`bd¢£swrc s{¢³o«dqrzj
udqJ`o^¨<jlubW~>d>zqrowjtu¯vnloC~dJynlow¤dJntd | ¤k} ¢Þo{mbntqryJRo{u | qzo{uyzj±qrjtsCuynpo{¤Fd>nld | ¤k} ownlowzc%yJ©«$dK~d>jl¨wd |
ownlowzc%yqrzjlwCd>qz`d(ubdqK<owu | ¨kjlyzj±qrjtuo¢Þo{mbntq}°vnloC~d$¡ swmbn| jtu | jl~Jo-qzd(qz`o{q:y[sCcAd#¢Þowmbntq:sx~>~mzrd | jlu
qr`bdsCzjlwjluownEubdq¢£sw³cswubjtqzsCzjlub©(ubswqz`bdJ³o{vvbzs<ow~`+¡ swmbn| ~sCuyzjly[qjluPdJy[qzjlc%o-qzjlubqz`bdA~mbrzdJu<q
c%owzÃkjlub°sw¢qr`bd0dqrzj&ubd>q$¢£sw$cswuj±qrswrjtubbowy#jlu Iù xTK5Iù w NK8©
sw$swm(o{vbvbnljp~>o-qrjtsCuEk¡dfubdJd | d | qzs%y[mvbvsC[q | jpy[qzrjt¤bmbqzd | ¢Þowmbn±qy$o{u | d>¨Cd>u<q$vbrswvowCo-qrjtsCuo{u |
| jly[qzrjt¤mxqzd | yzd>uy[sCy[d>qzmbvyJE¢£rswc ¡$`bjp~` ¡$rswujlu<qzdJznldJo^¨kjlub~Jo{u¬rdJyzmbn±qK©-H(dJu~d%¡ d¢£d>dJnRjtqjtcA
vFswzqrowu<qJEqr`o-q°zsC¤bmy[qzubdKyzyowCowjtuy[qo+¡$zsCub jluCqrd>rntdKo^¨kjtub+yz`bswmbn| ¤Fdo |b| zdKyzyzd | ©RH(s-¡ d>¨wdJJqz`bd
o^¨-owjtnpo{¤bnld(o{vvbzs<ow~`bdKyq}kvbjp~>o{nlnl}AoCyzyzmbcd(qr`o-q#o{npo{rcyo{rd(rdJ~dJjt¨Cd | jluyzd<mbd>u~dowu | qz`o-q:qr`bjpy yzd
<mbdJu~djpy owuow~qzmown zjlubAy[d Cmd>u~>d³sw¢Eqz`bdubd>qJbo{uowyry[mcAvbqzjlswu@ubswq#oC~>~>d>vxqo{¤bnld³jlusCmb#~swu<qrdkqJ©
nlyzs¢£sw0sCmbo{vvbntjp~>o{qzjlswu jtu¬¢Þowmbntqc%o{uowwd>cdJuCq0jlu qzd>nldJ~>swccmubjl~Jo-qrjtsCuy0ubd>q¡sCzÃxy =£¡$`bdJzd
¢Þowmbntqryowzd+q}kvbjp~>owntnl} qzo{uyzjtdJu<q ?¦$vzs-¨kj| jtu d>xvbnlowuo-qrjtsCuy%jlu qz`d ¢£swrc§sw¢%À r¶>µ ) ¦½Þº^À fubs{qmyq
yzuowvy[`s{qryJ¡#owydJyry[dJu<qzjpo{n8© jluowntnl}wFzd>qzmbrubjlubowntnyz~>d>uowzjlsCy(~>swcvo{qzjl¤bntd¡$j±qr`Pqz`dsw¤y[dJz¨-o-qrjtsCuyJ
¡#owy$qz`bdrd<mbjlrd>cd>u<q$¢£rswcsCvdJro{qzsCry#jlu ubdq¡ swrÃc%owuo{Cd>cd>u<qJ© _#`bd>} | j| ubs{qowyzÃ@¢£sw³o%cswrd
dJnlow¤sCro{qzd | jlux¢£swrc%o-qzjlswu+yzm~`oCy ¢Þo{mbntq(j| d>u<qzj ~Jo-qzjlswuxsw$jpy[sCnlo{qzjlswuE©
uAqz`jlyvowvdJJw¡d#vbrswvFsCyzd$o{uo{vbvbrsCoC~`0qzsf`owu | nld#mbuk¤sCmbu | d | oCy[}ku~`zsCu<}fjlu | jlyr~rdqrddJ¨wdJuCq
yz}xyqrd>c%y | jlowwubs<y[jpyE¤k}fmyzjtububdq#¸xµJ¹º{»t¼-½¾µk¿-ÀkswrjtCjtuowntnl}vzsCvs<y[d | ¤<}0¥© (jld>npyzd>uEA©KRnls{qzÃkjluE{o{u |
A©xª jluyzÃwdJn,Iù 7NK8©ux¢£swn| jlubCy ¡ d>rd³myzd | ¤k}P~ jtnlnpo{u I <7K&¢£sw#cs | d>n&~`bdK~Ã<jlubAjtu¨wdJzj ~>o{qzjlswuE©
_#`d>}¡ d>rdRyzmb¤yzd<mbd>u<qrnt} | d>¨Cd>nlswvFd | ¤k} @Ruwd>nt¢£rjtd>q It^ .KÒ^(swÌ>dJuk¤dJz$o{u | @:ubwdJn±¢£rjtd>q IbKÒ@:y[vo{rÌJob
owu
|
wcdJPItKK5Il>e*K5Il 5 K8© (dq°mbux¢£swn
|
jlubCyo{rdA¤rowu~`bjlub yqrzm~qzmbrdJy0yzmbjtqrow¤bntdqrsPrd>vbrdJyzd>u<qfqz`bd
yzdq+s{¢°dxdJ~>mxqzjlswuys{¢Ao²dqrzjfubd>qmy[jlub o{u4oCy[}ku~`zsCubswmyy[dJcowu<qzjp~>y¡$j±qr` nlsx~>o{n0y[qro{qzdJyo{u
|
vo{zqzjpo{nlnt} sw
|
d>rd
|
qrjtcdC©
u²qz`bjpyyqrzm~¦qzmzdCR~swccswu¥vzd bxdJy°s{¢(dxdK~mxqrjtsCuy°owzdy[`o{rd
|
o{u
|
d>xdJ~mbqzjlswuy | jVAFdJzjlubswubnl}PjluWqr`bdjtu<qrd>rntdKo^¨<jlubs{¢:qr`bd>jlqzo{uyzjtqzjlswu zjlubCyfowzdAzdJvbrdJyzd>u<qzd | swubnl}
sCu~dC© ´ mbcswqzjl¨^o{qzjlswuE¢£swmyzjtub dqzrjfubdqy+o{u | qz`bdJjt+mbux¢£sCn| jtub<y>jlyqzs`o^¨CdWo{u4d>nld>Cowu<q
cs | dJn sw¢³owyz}ku~`brswubsCmy, uj±qrd+y[qro{qzdcoC~`bjlubdJyJqz`d>rd¢£swrd¡ drdJy[qzrjp~¦qswmby[dJnt¨CdJyqzs«yro-¢£ddqrzj
udqry³qr`bzsCmbw`swmxqqz`bjpyfvowvdJJ© dqmbub¢£swn| jtuCyfo{rdubswq0¡dJntnt8Ãkubs-¡$uWjtu«qz`bd%~>swu<qzrswn~sCcAc°mbubjtq}w
qr`bd>}`o^¨wd¤Fd>d>u+`bs-¡ d>¨Cd> myzd | ¢£sw(yzmbvFd>r¨<jpyzswr}@~swu<qrzsCnFjluWI wKLI {eNK8©
_#`bdvo{vFd>jpyEswrCowubjlÌ>d | oCy&¢£sCntnls-¡(y>©hkdJ~qzjlswu° #jpy | d>¨Cs{qzd | qzsqz`bdvbzsC¤bnld>cy[d>q[qrjtub©hkm¤y[dK~¦qrjtsCu
b©t0~>swnlntdK~¦qry$qz`bdud>d | d | ¤ow~ÃkCzsCmbu | c%o{qzd>rjpo{nEsCud>qzrjEubdqyowu | qz`bdJjt(mux¢£swn| jlubCyJ© hkm¤y[dK~¦qrjtsCu
b© Pjtu<qrzs | m~>dJy°swmb yqdbowcAvntdC© (u | swmbAvbrsw¤bnld>c yzdqzqzjlubW¢£sCAoCy[}ku~`zsCubswmy | jpo{wusCyzjlyjly
¢£sCzc%owntjlÌ>d | jlu+yzmb¤yzdJ~qzjlswu x©bx¡$`bjp~` ~sCuyqrj±qrmxqzdKy#vdJyzdsCmb yq(~>swu<qzrjt¤mxqzjlswuE©
uowyz}ku~`brswubsCmy | jpo{CubsCyzjlyJ-y[sCcdrdJ~>sw | d | ownlowzcyzd<mbdJu~dKy | jVAXd>swunt}f¨kjloqz`d jlu<qzdJznldJo^¨kjlub
sw¢~sCu~mzrd>u<qownlowzc%yJ^`bd>u~>djtqjly | dKy[jlrow¤bnldubswqqrs | jly[qzjlubwmjlyz`°yzm~`°ownlowzcyzd<mbdJu~dKy>©hxjtcjlnlowznl}w
jtq:jpy | dKy[jlo{¤bnld$ubs{q:qzs | jpy[qzjlubwmbjpyz` | jlowwubs<y[dKy¡$`bjp~`%swubnl} | jBAXd>jtu%qr`bd(jlu<qzd>rnldJo^¨kjtusw¢E~swu~mbrzdJu<q
¢ÞowmbntqryJ©½*)>¿wµFº-À½pÀAµF¶>·ÞÀowzdjtu<qzrs | m~>d | qrs@qz`jlyd>u | jtu«y[dK~¦qzjlswu«bFqz`bdJ}+dxvbrdJyry$qz`d°yzswnlmxqzjlswuPsw¢
oCy[}ku~`zsCubswmy | jlowwubs<y[jpy$¤k} myzjtuyzmbj±qo{¤bnldmux¢£swn| jlubCyJ&o{u | ~>swuy[qzjtqzmbqzd°qz`bd°cowjtu ~sCuCqrzjl¤bmxqrjtsCu
sw¢qz`bjpyvo{vFd>K©#sCzrdJyzvFswu | jlub%o{nlwsCzjtqz`cyo{rd0wjl¨wd>u jluPyzdJ~¦qrjtsCu e©(_#`bdKy[d°o{nlwswrjtqz`bc%y$`o^¨Cdfqz`bd
¢£sCzcs{¢vo-qzqzd>ruco{qr~`bjlubrmbntdKy$o{u | o{vvbnt}owyz}<u~`bzsCubswmy[nl}w©
E% / .>(' E
u qr`bjlyy[dK~¦qzjlswu¬¡ d yq0jluCqrzs
|
m~dqz`d%¤ow~Ãkwrswmu
|
¡ d%ubd>d
|
swu¬dqzrjRubd>qryowu
|
qz`bdJjtmbux¢£swn
|
jlub<y>© _#`bd>u+¡ d0jtu<qzrs
|
m~>d0jtux¢£sCzc%owntnl}oCy[}ku~`brswuswmy
|
jpo{CubsCyzjly#sCu o{u+dbo{cvbnldw© (u
|
uo{nlnt}¡d
¢£sCzc%owntnl} | d ubdowyz}ku~`brswubsCmy | jlowwubs<y[jpy>©
!"#$%'&)(*"+#,!(-"+$./0"1!(2#3!456#$
#oCy[jp~fzd>¢£d>rd>u~>dJy$owzdPIù ,KLI7NKLItCK8©YH(sCcswcswrvb`bjpy[c%yJ~sCu+7jp~¦qK~sCu~mzrd>u~>}wowu | mbux¢£sCn| jlub<y>Fo{rd
qr`bd$dJyryzd>u<qzjpo{nb~>swu~>d>vxqyswuA¡$`bjl~`%o³qzrmbd$~sCu~mzrd>u~>}o{u
|
¢£mbnlnl}°owyz}ku~`brswubsCmy¨<jld>¡s{¢Fdqzrjbubd>qry
jpyR¤owyzd
| ©
u%sw
|
dJRqzsjtu<qzrs
|
m~>d$qz`bdKy[d³ubs{qrjtsCuyJwjtq¡$jlntnF¤d~sCu<¨Cd>ubjld>u<qRqrs~sCuyzj
|
dJRwdJubd>o{n udqry
jluqz`bdyzd<mbdJnI©
8 Å K
Ê É É É I¯:9 µF¶>·jlyoqzrjtvbnld;=<=>@?BAC!AEDGFC¡$`bdJzd!? o{u | Cowzd | jpyÞswjluCq
yzdqy:sw¢ 'F»)%¶¦Àfo{u | ·0){µbÀ¦½¾·I½Þº{µbÀ¦ko{u | DIHJ>K?MLNCF+OP>QCRLS?TFjpy:qz`bdU#ºWV r¶»){·I½Þº{µ _#`bdrdX7d>xjt¨Cd
qrrowuyzj±qrjt¨Cd#~>nts<y[mzd s{¢Fqz`bdB7s-¡²rd>npo-qzjlswuYD jpy | dJubs{qrd | ¤k}YZ0Cowu | jtqryRjtrzd[7dxjl¨wdqzo{uyzjtqzjl¨wd$~nlsCyzmbrd
jpy | d>ubswqzd | ¤k}]\0©«Rnpow~>dJyo{u | qzo{uyzjtqzjlswuy°o{rd~>owntnld | µFºK¼w¶À^$Cd>ubdJzjp~>owntnl} | d>ubswqzd | ¤<}^© bsw
^`_`?OTCC¡ d | dJubs{qrd¤k}baE^P<dcfebgWeSDh^2iqr`bd ' z¶¦À>¶>·:sw¢Xus | d^kowu | ¤k}S^ja<dcfebgW^PDheki³jtqry
'º^À¦·IÀ>¶· swlmHn?oOpC¡d°¡$zjtqzd a lq<=rNsWtvu a ^ o{u | l a <wrxsvtvu`^ a ©(u ºNG%ºNG%º* 'x½pÀG
¢£rswc ofubdq;4qzsoubdq;xykjlyRofc%owv,z3gv?)OCn{|kDq? y}OCyxyzm~`Aqz`o{q:~z>@?TFB]? yÞz>KCFGCyÞ
owu | ~¢£swd>¨Cd>r}Aus | d^s{¢*;@<qz`bdrdJy[qzrjl~qzjlswu%s{¢2z qrsSa[^jly o¤bjdJ~qzjlswu¤d>q¡dJd>upaX^owu | a[zB>Q^kFJ
owu | qz`bd0rdJy[qzrjl~qzjlswus{¢/z¥qzs^*ajpy$o°¤jdK~¦qzjlswu+¤Fdq¡ d>dJup^*afo{u | zB>K^kF a ©
@w^
Å Å Å
Kv9
_¡sAubs
|
dJy^ A^ yEs{¢o°ubdqB;Ëo{rd½¾µ º-µ U ½)·2F¡$rjtq[qzdJub^T^kyÒxj±¢qz`bdJzddxjpyq
|
jly[qzjlu~¦qAqzo{uy[jtqzjlswuyEAy_ CRyzm~`¥qr`o-qba%a y<Wo{u
|
bZ ^yZ ^kyÞ© ubs
|
dP^ jlyAjlu
À>¶>»¹ º-µ U½)>·Aj±¢^x^© (u º¸ r¶µ r¶ µF¶>·jly%o«ubd>q <m>bAAEDGFyro-qrjly[¢£}kjtubWqz`bd¢£sCntnls-¡$jtu
o |b| jtqzjlswuown&vbrswvFd>zqzjldJy
^`_MO g^x^ ubs%ubs | dfjly(jtu yzd>nt¢¾Ò~>swu+7jp~¦q
^p_!oO g^ \3^ Z jpy(oAvo{zqzjpo{nXsC
|
dJ
^`_"nO g$#cfeYgWeP\3^2i%#%&(' Z jpy$¡ d>nlnX¢£swmbu | d |
*) _" g$#a ) #,+.-
dJoC~`vnloC~df`owy$o{q$cAs<yq
swudjlubvbmbq$qzo{uyzj±qrjtsCu
ª d@¡$jlntn owyry[mcAdqr`o-qqz`bdyzdq°s{¢$cjtubjlc%o{nubs | dJys{¢/ jpy~>swu<qrowjtubd | jtu0owu | ¡d | d>ubswqzd%¤k}
cjlu2>,F$sC(cjtu2>1xF$qz`bjpy(cjlubjlcownyzdqK©#hkvFdJ~>j! F~fqzdJzc%yowzdfmyzd | qrs | jpyqrjtuwmbjpy[`+sx~>~>mbrzdJu~d0ubd>qry
¢£rswc wd>ud>o{n#ubdqy>©( jpyAqz`bdPyzdq%sw¢ º-µX¼-½¾·8½Þº-µbÀ 2 jpyAqz`bdPyzdq@sw¢¶0^¶>µ·IÀ T\jpyAqz`bd ){¸kÀ ){»½¾·
rd>npo-qrjtsCuE©
s | dJy^¥o{u | ^ yowzd3º-µ ¸ z¶>µ·2¡$rjtq[qzdJu ^33^ y8Ejt¢ubdJj±qr`bd> ^3Zd^ yIEubsw^3Zd^ y8EubsC^T^ky
`swn| © rº4ÒÀ>¶·(jpyoyzdql!sw¢:~sCu~mbrrd>u<q³~sCu | jtqzjlswuyJ© c%o-xjtc%ownJ=¾¢£sCyzdqjtu~nlmy[jlswu?(~swÒyzdq³jly
~Jo{nlntd | o ¸x· º-µ65¿w¸ 0)-·8½Þº-µ87jpy oAyzmb¤xÒubdq#s{¢9%x¡$`bjp~`jpy º-µfU ½)>·:¹r¶r¶ =£ubsAq¡ subs | dKy owzdjlu
~>swu+7jl~q ?¦o{u | )-¸kÀ )-»¾» »tº-À>¶r¼ =Þj±¢^ y-Z3^Powu | ^`_!7kqz`d>u)^ y2_"7?¦©
´ ~J~mbrzdJu~dfubd>qry³o{rdmy[d>¢£mbnEqrs%zdJvbzdKy[dJu<q#d>xdJ~mbqzjlswuy$sw¢d>qzrjEubdqy>©#_#`bdJ}o{rd0o%y[m¤F~>nloCyzy$sw¢
udqryJ&jlu«¡$`bjp~`WdKyzyzd>u<qrjlownvbrswvFd>zqzjldJyfowzd°¨<jpyzjt¤bnldA¨<jpoqz`bdAqzsCvsCntsCwjp~>owny[qzrm~¦qrmbzdAs{¢:qz`bd¤bjlvo{zqzjtqzd
Crowvb`E©
;³Å >* Å J:9 bsw; oAubd>qJboRG ) <-½¾µk¿%s{¢ ; jpy o°cmn±qrjlyzdq/= sw¢vbnpow~dKy>kj8©dC©tbo°c%o{v"= gv?d{|kD
c?>A@-vABAAC@CCiC©:ED$¶>·¦½µF¶>·Rjpy ovo{jl;d<w>;YAB=GFfF¦x¡$`bdJzd;Ájly o°ubdq `o^¨kjtub ubjtqzdfy[d>qrys{¢vnloC~dJy
owu | qzo{uy[jtqzjlswuyJowu | =HF@jpyowu ½¾µ½¾·8½*)-»$c%o{rÃkjtu© qzo{uy[jtqzjlswuHS_]C jpy¶>µ )»l¶r¼¯o-qc%o{rÃkjtu
= j±¢I= >KJjF"LM>P¢£sC%d>¨wdJz}!Jw_ a ¦© hkm~` o«qzo{uyzj±qrjtsCu ~Jo{uH5 z¶>:nldJo | jtuWqrs¬o ubdJ¡c%o{rÃkjtu
=Jy/<N= | a POQ}a{E¡d | dJubs{qrd°qr`bjpyf¤<}R=NS=JyI©°_#`dAyzdq0s{¢ z¶ )2 )»t¶@c%o{rÃ<jlub<ysw¢;jpyqz`bd
yzc%o{nlntdKyq =£¡0©J©qJ©yzdqjlu~>ntmyzjlswu?:y[d>q=HFTS~sCuCqo{jlubjlubU=HF³owu | yzm~`%qr`o-qV= _!=HFSRowu | =NS=Jy
qrswCdqz`d>Rjlcvbnt}W=Jy*_!= F S¦©dqrzjubdq; jpy$À )¹¶³jt¢X= >K?TFMc6>A@-Wi#¢£sw:d>¨wdJz}zdKow~`ow¤bntd#c%o{rÃkjtu
= © _#`zsCmbw`bsCmxqqz`bjpy%vowvdJJ ¡ dP~swuy[j| d>sCubnt}yzo{¢£d+d>qzrj(ubd>qryJ `d>u~>d cowzÃkjlubG= ~Jo{u ¤d
rd><o{ | d | oCyoPyzmb¤yzdqsw¢(vbnpow~dKy>© ubjtqzdsx~>~mzdJu~d@udqY ~>o{u²¤dzdJCo{ | d | oCyo d>qzrjubd>qJ
¡$`d>rd³qr`bd0jlubj±qrjlownEc%o{rÃkjtubAjpyZ= F <([]\_^2>`YF¦©
a - É Å K Å ¥ Ê &ÒÉ .ÞÊ :9 0){µk½¾µk¿ ' zº¶ÀÀ+sw¢³dqrzjubdq; jly@o vowjt
Y3<w>bYA}zFw¡$`bdJzd/ jpyo{uAsx~>~>mbzrd>u~d ubdqKCo{u | zWjlyowu`bswcswcsCzvb`jlyzc ¢£zsCcc4qrs;4rd>Cow | d |
oCy ubdqy>byzm~`qz`o{q$ ~fqz`bd0rdJy[qzrjp~¦qzjlswus{¢ z¯qzsAcjtu2>1xF$jly$o°¤bjdJ~¦qrjtsCu¤Fdq¡ d>dJucjlu2>bNF#o{u
| = F
=£qz`bd yzdqs{¢jtubjtqzjpo{nlnl}¥cowzÃCd
|
vbnloC~dKy^?:o{u
|
:~ ¢£sw%o{nlnVdAd y _e%Bad < a d y$o{u
|
zB>dFb< z>:d yF
qrswCdqz`d>fjtcvbnl}fdb<gd
y© }Wo{¤my[dsw¢ ubswqro{qzjlswuEE¡ d%y[`o{nln:y[sCcdqzjlcdJyf¡$rj±qrdcAjlu2>YBFjluy[qzdJo
|
sw¢
cjlu2>bNF¦©
_#`bd y[d>qs{¢bowntnC¤browu~`bjlub$vbrsx~dJyryzdJy&sw¢kd>qzrjwubd>q2; jlymbubj<mbd>nl} | d ubd | -mbvfqrso{u0jpy[sCcswrvb`bjpy[c
=ÞjI©dw©l$o¬zdJuo{cjlub¬s{¢qz`bd«~swu | j±qrjtsCuy%o{u | dJ¨wdJuCqy^? owu | ¡dPyz`owntn(us{q | jpyqrjtuwmbjpy[` jpy[sCcswrvb`bjp~
¤rowu~`bjlub°vzsx~dKyzyzdJyJ©bswVY AYByq¡s¤bo{u~`jtubAvbrsx~dJyryzdJyJTYByFjlyo ' z¶5+s{¢ Y<¡$rjtq[qzdJu"YyQY³
jt¢qr`bd>rd#dxjpyqyowu°jlu-dK~¦qzjl¨wd#`bsCcswcswrvb`bjpy[c ¢£rswcEYBykjtu<qrs Y{y[m~`qr`o-q>[]\^ >`YByF}F <([]\_^2>`YF¦
owu
|
qz`bd ~sCcvs<y[jtqzjlswu z ~sCjtu~>j
|
dJy¡$jtqz`]z
y
¡$`bd>rd
|
d>ubswqzdJyAqr`bd ~sCcAvFsCyzjtqzjlswu²sw¢³c%o{vy>©
}+qr`bd>sCzdJc {s{¢IlK .KÒ&qr`bd>rd°d>xjly[qryP=ÞmbvWqrsowuWjpy[sCcswrvb`bjpy[c ?³ombuj<mbdc%o-xjlcmbc ¤bo{u~`bjtu
vzsx~dKyzyow~>~>sw | jlubqzs0¡ d°~Jo{nlnjtq³qr`bd¸xµK¹º-»t¼{½¾µ<¿+sw¢;@Fowu |P| dJubs{qrdj±qf¤k}(©³_#`dmbux¢£sCn| jtub
sw¢ ;!vs<yzyzdJyry[dKyqz`dW¢£sCntnls-¡$jtu¥mbubjl¨wd>yro{nvzsCvdJ[q} «¢£swdJ¨wdJz}sx~>~mzrd>u~>d ubdq8%o{u | dJ¨wdJz}
`swcswcswrvb`bjpyzc`gT {D ;@kqz`bdJzdfd>kjpy[qry#o{u ½¾µ>¶>·I½b-¶`swcswcswrvb`bjpyzc gT={D(byzm~`qz`o{q
< z A =.?
¡$`d>rdYz | dJubs{qrdJyqz`bd@`swcswcswrvb`bjpyzc owyryzsk~>jlo{qzd | qrs(© dJ~>swcvs<y[jtqzjlswu =[.?fd>kvzdKyzyzdJyfqr`o-q
[c%o-xjtc%owntnl}+mbux¢£swn| y x;@© ¢;jlyfjtqryzd>nt¢o{u«sx~>~mzrd>u~>dubd>qo{u | =HF,< []\^2>Q;NF³`bswn| yJqr`bd>u
j| dJuCqrj! dJy$¡$jtqz`p;@©
³yo{uubswmbu~d | ~sCu Cmbro{qzjlswuyfowzd%o | d<mo-qrd%zdJvbrdJyzd>u<qro{qzjlswuys{¢ rjtu+yzd<mbdJu~dKy0s{¢#dqrzj
udq;@© 6Ed>q= F A= AB=WAC@CC¤FdPo¬c%o-xjtc%own zjlub¥y[d <mbd>u~>d+s{¢ ;@ owu | nldq=4 4S=«¤d
qr`bdoCyzyzsx~jpo-qzd
|
y[d Cmd>u~>d@s{¢ rd
|
qrrowuy[jtqzjlswuy>© _#`bdJu¬qz`bdJzd@d>xjly[qry°o mbubj<mbd@c%o-xjlcown =£¢£sw°yzdq
jlu~>ntmyzjlswu?:~swu wmbo-qrjtsCu 7@sw¢*;Á`o^¨kjtu0qz`bd³¢£swnlnls-¡$jtubvbzsCvdJ[qrjtdKy 7jly:qz`bdmbubjlswus{¢o°y[d Cmd>u~>d
d!Ad"AC@CCs{¢d>¨Cd>u<qry(owu
|
o%yzd<mbd>u~d$#
F
A%#&A'#(:AC@CCbsw¢~>mxqryJXy[m~`qr`o-qK¢£sC(dJoC~`*)!L >b zB>+#,vF<
=< z>:d-WFN< ko{u | #,.*/ ad- AdWa
0#,k© swuk¨wdJryzd>nl}wdJow~`¥c%o{kjlc%o{n ~swu wmbo-qrjtsCu¬s{¢B;
| d ubdKyo«c%o{kjlc%o{n rjtu yzd<mbdJu~dCR¡$`bjp~` jpyAmbubjCmdmv²qrsWqr`bd jtu<qrd>rntdKo^¨<jlubPsw¢y[qzrm~¦qrmbo{nlnt}
~>swu~>mbrzdJuCqqzo{uyzjtqzjlswuygqrrowuyzj±qrjtsCuyo{u | y o{rdy[qzrm~qzmbo{nlnt}%~>swu~>mbzrd>u<q#jBA a y >a jOW a F<
owu | a * >a y:O ya F <.x©
1$ .Å 9 jt©F yz`bs-¡(y#qr`bddbowcAvntd¡ d0¡$jlntnmy[dqz`brswmbC`bswmbq$qz`bjpy(vowvdJJ© d>qzrjubd>q!;
jpy0yz`bs-¡$u«sCuWqr`bd%nld¢¾qJ© qyfvbnpow~dKy0o{rd-:ABAA%2A%3A54+A%6A57xFowu | jtqry0qzo{uyzj±qrjtsCuyfo{rd8 A%898 A%898:85A%8:;kA ;kA ;<8©
:nloC~dJy$~>swuy[qzjtqzmbqzjlubqz`bd0jlubjtqzjpo{n&c%o{rÃkjtuowzdd>u~jlr~>ntd | jluqz`bjp~ÃX©
¤rowu~`bjlub%vbrsk~>dJyryY]< >1A z/F(s{¢/;Ëjly³y[`bs-¡$u+sCuqr`bdrjtC`<qJ© qry~>swu | j±qrjtsCuy(o{rd | dJvbjl~qzd |
¤k} ~jl~nldJyJFowu | jtqryd>¨Cd>u<qry³o{rd wmzd | ¤k}¤Fs^xdJyJ©@:oC~`W~sCu | jtqzjlswu ) s{¢Y4jly³nlow¤dJntd | ¤k}`zB>) FXo
vnloC~ds{¢-;@©@:oC~`dJ¨wd>u<qVdfs{¢XY jpy nlow¤dJntd
|
¤k}YzB>dF¦bo°qrrowuy[jtqzjlswus{¢2;@©: ~sCu Cmbro{qzjlswu%sw¢dqrzj
udq ; jlyyz`bs-¡$u¬jlu CzdJ}w© s{qrdqz`o{qqz`bdcAjlubjlc%o{n:~>swu
|
jtqzjlswu¬npo{¤Fd>nld
|
¤k}=7jpy0¤bo{u~`jtub+jluGY³
own±qr`bswmw`@jtq$jly ubswq ¤bo{u~`bjtujlub; jtqryzd>nt¢©R_#`bdzdKowyzswu%jpy qz`o{qJkjlub;@<qz`d³qrswÃCd>u~Jo{u@¢£rd>dJnt}%cs-¨Cd
owntsCubfqz`d~>jt~mbjtq -D?>@> D A D?>@>@> D -wko{u | zdKy[}ku~`zsCubjtÌJd(o-¢¾qrd>r¡ ow | yR¡$j±qr`%qz`bd³qzsCÃwdJu@y[jtq[qrjtub
jluA7k©
_#`bdcAdK~`o{ujlyzc ¢£sC:~sCuy[qzrm~¦qrjtubfqr`bd(mbub¢£swn| jtus{¢&dqrzjubdq ;jpyjlntnlmy[qzo-qzd | jtuqr`bd(cj|b| nldw
jtq#jlyjtub¢£swrcowntnl}dxvbnpo{jlubd | owy:¢£swnlnts-¡(yJ©:mxqqr`bd³qz`brd>d~swu | j±qrjtsCuynlow¤dJntd | ¤k}Aqz`bdjtuj±qrjlownc%o{rÃkjtu
sw¢;@qz`jlyAjpyqr`bdcjlubjlcown#¤browu~`bjlubWvzsx~dKyzys{¢!;@©¬_#`bdJuE¢£swAdJoC~`²~sCuy[qzrm~¦qrd | ¤bo{u~`bjtu
vzsx~dKyzy/Y³&yzd>nldJ~qfo~s{®yzdql§s{¢9YX¡$`bjl~`«jlynpo{¤Fd>nld | ¤<}qr`bd°vzdKy[d>qTa (s{¢ y[sCcAdqzo{uyzjtqzjlswu8(sw¢
;@bowu | `owy#ubsdJ¨wd>u<q#nlow¤dJntd | ¤<} :jlujtqry#vFsCy[qryzdq$¡$jtqz`bjlu"Y³©:vbvdJu | qzsSl o°udq(jpy[sCcAsCzv`bjl~qzs
a SD D }a=£rdJ~Jo{nlnxqz`o{qzB>a F<Rl ?¦ko{u | npo{¤Fd>nj±qy:o || j±qrjtsCuo{nubs | dJyR¤<}o{u | }a{<zdKy[vFdJ~qzjl¨wd>nl}w©
dJ[¢£sCzcjlub%qz`jly³zdK~mbyzjt¨Cd>nl}}kjtdJn| y³owntnvs<yzyzjl¤bntd ubjtqzdA¤bo{u~`bjlub%vbrsx~dKyzyzdJys{¢;@©³_#`d>jl³mbujtsCu
jpy qz`d0mbux¢£swn| jlub$©
7 iv 5 3 7 1
4 2
3 2
i i
3 2 1 1 4
3
i i
1 1
2 3 4
7 5 6
2
4
6 5 1 7
1 ii
v vi
1 1
7
iii
1
iv
4 ii
iii i
1 7
4
2 3
5 6
iii iv v
vi
iii iv v
iii
jlwmbrd N+;(T)b/ +T% &' b+./^#%'&:; #66 +&N6-+ b+&#B& "%00$$ Q#7/ 0<N%3 /#$
+&N6 $T.$ .*&7/N+;0$71 / +4 / )Q%!%1\#B&"T% &7!&./^#%'& )Q%3 36 b+T1 #B&$#'T/ #*&.0/:$,+&N6 %%N 2 &&T
&T/:$.<('B&#'0/ Q#E&.0/:$/)3%1 +./^#% &(#$\6*#/:.6 .$#B&*+!,.-/0.-*21&,3,54%6879:'V&(% 5 &&T &.0/:$3$#B&0
&%$T9% $/")C%1 +./^#% &<;,=4>?,.-@77-@7A*B4%6DCE681&,3*&7F3+&6(/.* "0)Q%3 " / X#$ &% &0.68/:%G' "
/; !*#+86C#B "/:.6P+ 5 "%1 $3$ /+&6+ b6 $ %#6#B&.7$Y+* .$ 76-#B&$:/:7+N6<
/
x
Å .Å Ê Å
J Ê
Å
Þ
É Ê {Kv9
swx; < >@?BAC!AEDGFoPubd>qJo¥»)r¶>»½¾µk¿¥jpyo c%o{vIHog
Co{|kDKJx¡$`bd>rdJ jly$yzswcd ubjtqzdowntvb`o{¤FdqJ©: ubd>qB;=<=>K?BACA5DoA@HkF d<mbjlvbvd
|
¡$j±qr`+o°npo{¤Fd>nljtub
HWjpy~>owntnld
|
oP»)*¶>»t¶¼µF¶>· bsw;AL< c ?MLACNL AEDOL}A@H?L i< 8<c-:ABAbbq¡ s%nlow¤dJntd
|
ubdqy>qz`d>jlvbrs
|
m~¦q
; LP; fjpy qz`bd0npo{¤Fd>nld | ubd>q | d ubd | owy ¢£sCntnls-¡(y
; LP; < >@?BAC!AEDRAPH F C =I *?
uM=8 *?¦?d<n? RQp?{b¡$`d>rdQ | dJubs{qrdJy qz`d | jlyÞswjlu<q(mbubjlswuEbowu |
C <
c@%_pC gH>%[F_SJ UT(J Wi =Þj?
O c>`%WA fF_)C LpCgH W>`%fF <VH :>fFEi =Þjtjb?
O c@_pCgH v> F_SJ WT(J iA >\\_\F
JPD jVA
J`_)?o{u
|
JPD %¢£sw(~Jowyzd =Þjtjb?#sCX=Þj?
J`_)?0o{u
|
JPD 2¢£sw(~Jowyzd =Þjtjb?#sCX=Þjtjljb?
DMJ jVA
J`_)?o{u | %D PJ ¢£sw(~Jowyzd =Þjtjb?#sCX=Þj?
J`_)? o{u | D J ¢£sw(~Jowyzd =Þjtjb?#sCX=Þjtjljb?
